We know that the maximum number of basic solution of a linear system is given by nCm where n is number of unknowns and m is the rank of coefficient matrix and also of augmented matrix. By setting (n-m) variables equal to zero we obtain a basic solution. But if the question gives a solution and asks to check if the solution is basic then how should I approach? Finding all the nCm basic solution and checking can be very lengthy procedure.

  • $\begingroup$ What exactly is a “basic solution?” $\endgroup$ – amd Jul 14 '18 at 19:30
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    $\begingroup$ There are two facts you can use: (1) the number of basic and non-basic variables is known in advance, (2) any variable not at its bound is basic. There still may be some ambiguity left (this is the result of degeneracy). $\endgroup$ – Erwin Kalvelagen Jul 15 '18 at 15:40
  • $\begingroup$ see math.stackexchange.com/questions/2751676/… $\endgroup$ – LinAlg Jul 15 '18 at 18:24

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